a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.
How to analyse a linear function of calorie gain in terms of the exercise time
In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.
Now we proceed to respond the questions of the part a):
(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.
b) And lastly we calculate the amount of calories by evaluating the function:
T = 2000 + 500 · 3
T = 2000 + 1500
T = 3500
We should consume 3500 calories to spend three hours exercising.
Remark
The statement is incomplete, the complete form is shown below:
You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 + 500 · h
a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h
b) If you spend 3 hours exercising, how many calories should you consume?
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follow the steps to construct a diagram:
1:create points A, B, and C in order on a horizontal line with a distance of four units between successive points.
2:draw Circle with center that passes through b, and two tangents to the circle passing through C.
3:locate the points of intersection of the tangents with the circle, and labeled them D and E.
4: draw the radii AD and AE to create central angel EAD.
Take a screenshot of your construction, and paste it below.
Answer:
a=3=8
Step-by-step explanation:
there is none
The construction forms a diagram consisting of a circle, two tangents, and a central angle EAD as shown in the attached figure.
Construction is a topic that requires drawing a required shape, line, and figure with constructing tools. The appropriate steps should be taken so as to complete the required figure.
In the given question, the circumference of the required circle passes through points A and C. And the radius of the circle with center B is 4 units so its diameter is 8 units. Then joining the points D and E to A, creates a central angle EAD.
Following the appropriate steps, the required diagram for the construction is as given in the attachment to this question.
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EASY POINTS
Which of the following exponential functions represents the graph below?
Answer: It's B.
Step-by-step explanation: It can't be A or D. The y-intercept is 2, not 4 so it is B.
Which one of these functions is a quadratic function?
OA Rx) = x-3x+1
OB. f(x)=3*
OC. f(x)=x²³
OD. f(x) = log(x+7)
Answer:
x^2 -3x+1
it is your answer
The function x² - 3x + 1 represents a quadratic function.
A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are constants.
In option A, we have f(x) = x² - 3x + 1, which fits the form of a quadratic function with coefficients a = 1, b = -3, and c = 1.
In option B, the function is Exponential.
In option C, the function is Exponential.
In option D, the function is logarithm.
Therefore, x² - 3x + 1 represents a quadratic function.
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IK
rying the Distributive Property
Try it
Which statement is an example of the distributive property?
O3+ (2)(15)= 3(2) + 3(15)
O3(2+15) = 3 + 2(3) + 15
O3(2+15)= 3(2) + 3(15)
O 3(2+15)= 3(2) + 15
The statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
How to determine the example?The distributive property states that:
a(b + c) = a(b) + a(c)
Using the above property, we have:
3(2+15)= 3(2) + 3(15)
Hence, the statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
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3t-2/4 - 2t-3/3 = 2/3 - t
The value of the variable t will be 13 / 12.
What is Algebra?The analysis of mathematical representation is algebra, and the handling of those symbols is logic.
The equation is given below.
3t - 2/4 - 2t - 3/3 = 2/3 - t
Then the value of t will be
t - 3/2 = 2/3 - t
2t = 2/3 + 3/2
2t = 13 / 6
t = 13/12
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Use the commutative property of addition to write an expression equivalent to the following.
5a + b
The answer is
Explanation:
The commutative property of addition is where we can add two numbers in any order.
The general equation is x+y = y+x
A more concrete example would be something like 2+3 = 3+2 since both sides simplify to 5.
For 5a+b, it is the same as b+5a. We swap the two terms.
what's the answer to this
Step-by-step explanation:
the angle CDB is the supplementary angle to 9x+10 (angle ADC).
that means they stand together for 180°. as all angles around a single point on one side of a line are together always 180°.
and then, the sum of all angles in a triangle is always 180°.
so,
CDB + (4x + 10) + 50 = 180
CDB = 180 - (9x + 10) = 180 - 9x - 19 = 170 - 9x
therefore,
(170 - 9x) + (4x + 10) + 50 = 180
170 - 9x + 4x + 10 + 50 = 180
-5x = -50
5x = 50
x = 10
angle CDB = 170 - 9x = 170 - 90 = 80°
Una camioneta transportaba 3/4 de tonelada de arena para entregar a diferentes clientes. Si al primer cliente le dejo 1/3 de la carga que fracción de toneladas quedo en la camioneta
can someone help me with this worksheet please!!!!
(1) The missing term in the sequence, a₁₂ = 0.8.
(2) The missing term in the sequence, a₈ = 102.5.
(3) The missing term in the sequence, a₈ = 111.
(4) The missing term in the sequence, a₁₂ = -19.
(5) The missing term in the sequence, a₁₂ = 94.
(6) The missing term in the sequence, a₆ = 40.
(7) The missing term in the sequence, a₃₆ = -52.
(8) The missing term in the sequence, a₂₁ = -58.
Missing term of the sequenceThe missing term in the sequence is determined as follows;
Tₙ = a + (n - 1)d
1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?T₄ = a + 3d
18.4 = a + 3d ---(1)
T₅ = a + 4d
16.2 = a + 4d ---(2)
subtract (1) from (2)
-2.2 = d
18.4 = a + 3(-2.2)
a = 25
a₁₂ = a + 11d
a₁₂ = 25 + 11(-2.2)
a₁₂ = 0.8
2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?a₂ = a + d
57.5 = a + d -- (1)
a₅ = a + 4d
80 = a + 4d --- (2)
solve (1) and (2)
d = 7.5
a = 50
a₈ = a + 7d
a₈ = 50 + 7(7.5)
a₈ = 102.5
3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?a₁₀ = a + 9d
141 = a + 9d --- (1)
a₁₃ = a + 12d
186 = a + 12d --- (2)
Subtract (1) from (2)
d = 15
a = 6
a₈ = a + 7d
a₈ = 6 + 7(15)
a₈ = 111
4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?a₂₂ = a + 21d
-49 = a + 21d ---- (1)
a₂₅ = a + 24d
-58 = a + 24d --- (2)
subtract (1) from (2)
d = -3
a = 14
a₁₂ = a + 11d
a₁₂ = 14 + 11(-3)
a₁₂ = -19
5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?a₄ = a + 3d
-2 = a + 3d --- (1)
a₈ = a + 7d
46 = a + 7d ---- (2)
Subtract (1) from (2)
d = 12
a = -38
a₁₂ = a + 11d
a₁₂ = -38 + 11(12)
a₁₂ = 94
6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?a₉ = a + 8d
64 = a + 8d --- (1)
a₁₂ = a + 11d
88 = a + 11d --- (2)
Subtract (1) from (2)
d = 8
a = 0
a₆ = a + 5d
a₆ = 0 + 5(8)
a₆ = 40
7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?a₂₀ = a + 19d
-4 = a + 19d ---- (1)
a₂₃ = a + 22d
-13 = a + 22d --- (2)
Subtract (1) from (2)
d = -3
a = 53
a₃₆ = a + 35d
a₃₆ = 53 + 35(-3)
a₃₆ = -52
8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?a₂₈ = a + 27d
5 = a + 27d ---- (1)
a₃₃ = a + 32d
50 = a + 32d --- (2)
Subtract (1) from (2)
d = 9
a = -238
a₂₁ = a + 20d
a₂₁ = -238 + 20(9)
a₂₁ = -58
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To best show a possible linear trend in a scatter plot, draw a _________________.
A. regressive line
B. line of best fit
C. vertical line
D. horizontal line\
Answer:
b. line of best fit
4 The angle of elevation of point P from point Q is 40°. PQ = 45 km. How high is point P above the level of point Q?
Answer: [tex]45\sin 40^{\circ} \approx 28.925[/tex] km
Step-by-step explanation:
[tex]\sin 40^{\circ}=\frac{x}{45} \\ \\ x=45 \sin 40^{\circ} \approx 28.925[/tex]
The height of point P above the level of point Q is given by trigonometric relations h = 34.7 km
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let's call the height of point P above the level of point Q as h.
We know that the angle of elevation of point P from point Q is 40°, which means that the angle between the horizontal line passing through Q and the line segment connecting Q and P is 40°.
We also know that PQ = 45 km, which represents the distance between Q and P.
Using trigonometry, we can set up the following equation:
tan(40°) = h / 45
Solving for h, we get:
h = 45 x tan(40°) ≈ 34.7 km
Therefore, point P is approximately 34.7 km above the level of point Q
Hence , the height is h = 34.7 km
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Elaina Kicks A Soccer Ball With An Initial Velocity Of
By using the motion equations, we conclude that she will make the goal.
Will she make the goal?
First, we know that the goal is 20ft away, and the position in x is given by:
[tex]x = 28*cos(58)*t[/tex]
Let's find the time in which the ball will travel these 20 ft.
[tex]20 = 28*cos(58)*t[/tex]
[tex](20)/(28*cos(58)) = t = 1.35[/tex]
So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.
The height equation is:
[tex]y = -16*t^2 +28*sin(58)*t[/tex]
Evaluating in t = 1.35 we get:
[tex]y = -16*(1.35)^2 +28*sin(58)*1.35\\\\y = 2.9[/tex]
And the goal is 5ft tall, so we can conclude that she will make the goal.
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where do banks get the money to lend to consumers
Answer:
Depositors
Step-by-step explanation:
Answer:
Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.
what is two significant digit for 59.3506494?
Answer:
59
Step-by-step explanation:
Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.
help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
Write the prime factorization of 10
Answer:
2|10
5|5
1
Prime factors of 10 are 2*5
A freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded onto the elevator
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than
Answer:
2
Step-by-step explanation:
the same as...
(2) is the answer
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
What is the central limit theorem?The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
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Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile.
10, 15, 19, 23, 30
Part 1 of 6
The percentile rank for the value 10 is
The percentile rank for 10 will be 10th.
What is percentile rank?The percentile rank of a particular score in statistics refers to the percentage of scores in the frequency distribution that are smaller than that score.
Percentile rank = [(Number of values below x) + 0.5]/ total number of values * 100
For 10,
Percentile rank = {[0 + 0.5]/5} x 100 = 10th
For 15,
Percentile rank = ([1 + 0.5]/5) x 100 = 30st
For 19,
Percentile rank = [2 + 0.5]/5 x 100 = 50th
For 23,
Percentile rank = [3 + 0.5]/5 x 100 = 70th
For 30,
Percentile rank = [4 + 0.5]/ 5 x 100 = 90th
The percentile rank for 10 will be 10th.
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The following diagram shows a 4-step process that begins with Operation 1 and ends with Operation 4.
Based on the operations and their times, the capacity of this process is 10 per hour and the action that would yield the greatest increase would be 2. increase operation 2 by 14%.
What is the capacity of the process?The capacity of the process is the least operation time in the process which is 10/ hr.
How can we get the greatest increase in process capacity?Check all the alternatives given. The alternative with the lowest capacity is best.
Increase operation 1 by 12%:
= 11 x (1 + 12%)
= 12.32 per hour
Increase operation 2 by 14%:
= 10 x (1 + 14%)
= 11.4 per hour
Increase operation 3 by 10%:
= 12 x (1 + 10%)
= 13.2 per hour
The best alternative is therefore to increase operation 2 by 14%.
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If a 6-foot-tall baby giraffe casts a 4- foot-long shadow, then how tall is an adult giraffe that casts a 10-foot shadow?
Answer:
8- foot shadow? i am not sure
Answer:
i believe its 12 feet!
Step-by-step explanation:
assuming that the difference from the 6 foot giraffe with a four foot shadow is two feet, the 10 foot shadow would be two feet less then the giraffes height.
Let f(x)=20/5+6e^−0.1x What is (5)? Round your answer to 4 decimal places.
We can conclude that the function evaluated in x = 5 is equal to 2.3150
How to evaluate the function?Here we have the function:
[tex]f(x) = \frac{20}{5 + 6e^{-0.1x}}[/tex]
And we want to evaluate in x = 5, this just means to replace the x by a 5 in the given function:
We can evaluate this with a calculator (as doing it by hand is kinda hard), we will get:
[tex]f(5) = \frac{20}{5 + 6e^{-0.1*5}} = 2.3150[/tex]
So we can conclude that the function evaluated in x = 5 is equal to 2.3150.
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In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
The complete figure is attached with the answer below.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.
Cos(x)= Base / Hypotenuse
Cos(x) = ( 4.3 / 6.7 )
(x) = Cos⁻¹ ( 4.3 / 6.7)
Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
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Answer:
The answer is A
Step-by-step explanation:
Just took the test
#18 please I’m not good at math at all
Answer:
The answer is in the picture.
Step-by-step explanation:
By hand, you can factor it. I did it on a website called Cymath.
Answer:
3x(y - 3)(y + 1)
Step-by-step explanation:
Factor 3x out of 3xy^2
Factor 3x out of -6xy
Factor 3x out of -9x
Factor 3x out of 3x(y^2)+3x(-2y)
Factor 3x out of 3x(y^2-2y) + 3x(-3)
After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?
well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]
Answer:
Answer is 7% sales Tax
Step-by-step explanation:
I first like to take one percent of the original value, in this case 1% of 600 is 6 dollars. I then multiply 6 by the number needed to get to 642, which is 107- you will always then subtract 100 from this number and you get 7%. This should work for other problems as well. This is probably not the best explanation btw
if x+7y=16 and 3x-7y=4 what is the value of x
Answer:
[tex]x=5\\[/tex]
Step-by-step explanation:
First, put your equations into a system.
[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]
Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.
[tex]4x=20[/tex]
Lastly, divide by 4 on both sides to get x by itself.
[tex]x=5\\[/tex]
Solve the inequality |a + 3| > 14
Answer:
a∈(-∝;-17)∩(11;+∝).
Step-by-step explanation:
|a+3|>14; ⇔ 14<a+3<-14; ⇔ 11<a<-17;
You can buy a car for $5995.67 cash or pay $759.00 as a down payment and $129.95 a month for 4 years.
How much more does the installment plan cost than paying cash?
A. $1000.93
B. $241.93
C. $507.43
D. $2475.27
E. $99.27
well, if you had the cash right now, you can put it down cold for 5995.67 bucks
OR
put as a downpayment now 759 and then over 48 months pay 129.95 each month, well, 129.95 48 times is 129.95 * 48 = 6237.6, now let's add the 759 down and that's 6237.6 + 759 = 6996.6.
well, heck if you had the cash it'd be 5995.67, if you don't is 6996.6, their difference is 6996.6 - 5995.67 = 1000.93.
Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.
The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].
What is the slope of a straight line?A slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.
The slope of a line that passes through points ( p,q) and (x,y)
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
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If 0 lies in the quadrant IV. What can be the value of cos 0 ?
Answer:
the value of cos 0 is 7
Step-by-step explanation:
because you have to times it twice
Answer:
Between 0 and 1
Step-by-step explanation:
Cos Θ is the x coordinate of the unit circle. The points of that circle in quadrant IV have an x coordinate of 0≤x≤1.